9,569 research outputs found
A priori probability that a qubit-qutrit pair is separable
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact
computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures
volume of mixed quantum states" to refine our conjecture
Electron shielding of the nuclear magnetic moment in hydrogen-like atom
The correction to the wave function of the ground state in a hydrogen-like
atom due to an external homogenous magnetic field is found exactly in the
parameter . The projection of the correction to the wave
function of the state due to the external homogeneous magnetic field
is found for arbitrary . The projection of the correction to the
wave function of the state due to the nuclear magnetic moment is
also found for arbitrary . Using these results, we have calculated the
shielding of the nuclear magnetic moment by the electron.Comment: 15 page
Evaluation of Scheduling Methods for Multiple Runways
Several scheduling strategies are analyzed in order to determine the most efficient means of scheduling aircraft when multiple runways are operational and the airport is operating at different utilization rates. The study compares simulation data for two and three runway scenarios to results from queuing theory for an M/D/n queue. The direction taken, however, is not to do a steady-state, or equilibrium, analysis since this is not the case during a rush period at a typical airport. Instead, a transient analysis of the delay per aircraft is performed. It is shown that the scheduling strategy that reduces the delay depends upon the density of the arrival traffic. For light traffic, scheduling aircraft to their preferred runways is sufficient; however, as the arrival rate increases, it becomes more important to separate traffic by weight class. Significant delay reduction is realized when aircraft that belong to the heavy and small weight classes are sent to separate runways with large aircraft put into the 'best' landing slot
Departure Trajectory Synthesis and the Intercept Problem
Two areas of the departure problem in air traffic control are discussed. The first topic is the generation of climb-out trajectories to a fix. The trajectories would be utilized by a scheduling algorithm to allocate runways, sequence the proposed departures, and assign a departure time. The second area is concerned with finding horizontal trajectories to merge aircraft from the TRACON to an open slot in the en-route environment. Solutions are presented for the intercept problem for two cases: (1) the aircraft is traveling at the speed of the aircraft in the jetway; (2) the merging aircraft has to accelerate to reach the speed of the aircraft in the en-route stream. An algorithm is given regarding the computation of a solution for the latter case. For the former, a set of equations is given that allows us to numerically solve for the coordinate where the merge will occur
On Metric Dimension of Functigraphs
The \emph{metric dimension} of a graph , denoted by , is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let and be disjoint copies of a
graph and let be a function. Then a
\emph{functigraph} has the vertex set
and the edge set . We study how
metric dimension behaves in passing from to by first showing that
, if is a connected graph of order
and is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure
Ground state of two electrons on concentric spheres
We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79},
062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on
concentric spheres with different radii. The strengths and weaknesses of
several electronic structure models are analyzed, ranging from the mean-field
approximation (restricted and unrestricted Hartree-Fock solutions) to
configuration interaction expansion, leading to near-exact wave functions and
energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the
asymptotic expansion for the large-spheres regime are also considered. We also
study the position intracules derived from approximate and exact wave
functions. We find evidence for the existence of a long-range Coulomb hole in
the large-spheres regime, and infer that unrestricted Hartree-Fock theory
over-localizes the electrons.Comment: 10 pages, 10 figure
Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities
Characters and linear combinations of characters that admit a fermionic sum
representation as well as a factorized form are considered for some minimal
Virasoro models. As a consequence, various Rogers-Ramanujan type identities are
obtained. Dilogarithm identities producing corresponding effective central
charges and secondary effective central charges are derived. Several ways of
constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction
Quantum communication and state transfer in spin chains
We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation
The value-added of primary schools: what is it really measuring?
This paper compares the official value-added scores in 2005 for all primary schools in three adjacent LEAs in England with the raw-score Key Stage 2 results for the same schools. The correlation coefficient for the raw- and value-added scores of these 457 schools is around +0.75. Scatterplots show that there are no low attaining schools with average or higher value-added, and no high attaining schools with below average value-added. At least some of the remaining scatter is explained by the small size of some schools. Although some relationship between these measures is to be expected – so that schools adding considerable value would tend to have high examination outcome scores – the relationship shown is too strong for this explanation to be considered sufficient. Value-added analysis is intended to remove the link between a schools’ intake scores and their raw-score outcomes at KS2. It should lead to an estimate of the differential progress made by pupils, assessed between schools. In fact, however, the relationship between value-added and raw scores is of the same size as the original relationship between intake scores and raw-scores that the value-added is intended to overcome. Therefore, however appealing the calculation of value-added figures is, their development is still at the stage where they are not ready to move from being a research tool to an instrument of judgement on schools. Such figures may mislead parents, governors and teachers and, even more importantly, they are being used in England by OFSTED to pre-determine the results of school inspections
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